کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4597469 | 1336217 | 2009 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On the order bound of one-point algebraic geometry codes On the order bound of one-point algebraic geometry codes](/preview/png/4597469.png)
Let S={si}i∈N⊆NS={si}i∈N⊆N be a numerical semigroup. For each i∈Ni∈N, let ν(si)ν(si) denote the number of pairs (si−sj,sj)∈S2(si−sj,sj)∈S2: it is well-known that there exists an integer mm such that the sequence {ν(si)}i∈N{ν(si)}i∈N is non-decreasing for i>mi>m. The problem of finding mm is solved only in special cases. By way of a suitable parameter tt, we improve the known bounds for mm and in several cases we determine m explicitly. In particular we give the value of m when the Cohen–Macaulay type of the semigroup is three or when the multiplicity is less than or equal to six. When SS is the Weierstrass semigroup of a family {Ci}i∈N{Ci}i∈N of one-point algebraic geometry codes, these results give better estimates for the order bound on the minimum distance of the codes {Ci}{Ci}.
Journal: Journal of Pure and Applied Algebra - Volume 213, Issue 6, June 2009, Pages 1179–1191